So basically I am looking for a function which would map the score to the index. I have tried with logs and algebraic functions (is that the term?) but since the intervals are not the same (5 for the first, 10 for the second, 10 for the third, &c.) I don't know how to get around this.

Could you explain how the method works for constants $c_1,\dots,c_{n}$ and intervals $C_1,C_2,\dots,C_n$?
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Pedro Tamaroff♦Sep 28 '12 at 16:25

Is this function always increasing? I would guess yes...
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rubikSep 28 '12 at 16:37

1

Any function $f:\{1,\ldots,n\}\to\mathbb R$ can be written as $\sum_{k=0}^{n-1}a_k\left\lfloor\frac{x+k}n\right\rfloor$ by taking $a_k=f(n-k)-f(n-k-1)$. Of course summands with $a_k=0$ can be dropped, and sometimes you can simplify.
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Hagen von EitzenSep 28 '12 at 16:51